Document EP 0,172,561 discloses a postage meter of that type, in which the second print means are constituted by a thermal print head controlled by a microprocessor. The thermal print head is organized so as to move substantially transversely relative to the conveyor path along which the mail items to be franked advance. As a result, the mail item must be slowed down as it goes past the print head so that the auxiliary postage data is printed correctly, and this reduces the throughput of the postage meter.